Section 1.5 - Limits at Infinity
In a very fundamental way, limits are the core concept in calculus. Practically everything we discuss from here out is going to be defined in terms of a limit. In this section, we're going to use limits to define a class of functions that are what we call "continuous". These functions are well-behaved in the sense that they don't have any gaps, breaks or jumps. These functions are going to be the main ones that we're interested in throughout the rest of the class.
Videos
Lectures
First the definitions - and there are several. Continuous functions are the primary functions we're interested in in Calculus but there are several concepts we need to define to apply them. In the next lecture, we'll take these definitions and look at specific examples and applications. (lecture slides)
Now that we have a working definition of continuity, we can look at some specific examples to see how to apply it. (lecture slides)
The last lecture took a very concrete look at continuity by looking at specific functions. Now, we're going to take a step back and look at some more general statements. (lecture slides)
